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Beliebt Rechnen >

derivative f(x)=(x^2+3)(x^2-3)x^2

Lösung

ableitung von

f (x) = (x^{2} + 3) (x^{2} - 3) x^{2}

Lösung

6 x^{5} - 18 x

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + 3) (x^{2} - 3) x^{2})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2} + 3, g = (x^{2} - 3) x^{2}

= \frac{d}{d x} (x^{2} + 3) (x^{2} - 3) x^{2} + \frac{d}{d x} ((x^{2} - 3) x^{2}) (x^{2} + 3)

\frac{d}{d x} (x^{2} + 3) = 2 x

\frac{d}{d x} ((x^{2} - 3) x^{2}) = 4 x^{3} - 6 x

= 2 x (x^{2} - 3) x^{2} + (4 x^{3} - 6 x) (x^{2} + 3)

Vereinfache

2 x (x^{2} - 3) x^{2} + (4 x^{3} - 6 x) (x^{2} + 3) : 6 x^{5} - 18 x

= 6 x^{5} - 18 x

Graph

Beliebte Beispiele

limit as x approaches-2 of x+1

x \to - 2 lim (x + 1)

derivative (60)/(0.01x^2+1)

d er i v a t i v e \frac{60}{0.01 x ^{2} + 1}

limit as x approaches 2 of sqrt(((2x^2+1))/((3x-2)))

x \to 2 lim (\frac{( 2 x ^{2} + 1 )}{( 3 x - 2 )})

derivative y=16^{sin(x^2)}

d er i v a t i v e y = 1 6^{s i n (x^{2})}

steigung (2.3)(-2.3)

s l o p e (2.3) (- 2.3)